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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 16

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

Ratio Proportion

Problem

After A has finished 1/2 of a piece of work in 10 days; B joins him after 5 days. Later A completes the work in 4 more days. In how many days would B alone complete the work?

  1. 7\frac{1}{2} days
  2. 16\frac{2}{3} days
  3. 33\frac{1}{3} days
  4. 100 days
  5. 120 days

The Usual Method

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If A finishes 1/2 of the work in 10 days, it would take 20 days for A to finish the work alone. Assume that B takes ‘2’ days to complete the work alone. Thus in 1 day, B will do \frac{1}{b} of the work. So, in 5 days, B will finish \frac{5}{b} of the work.

Work done by A in 5 days = \frac{5}{20}=\frac{1}{4}

Work done by A in 4 days = \frac{4}{20}=\frac{1}{5}

The work done by A & B in sequence as mentioned in the question is:

\frac{1}{2} (by A) + \frac{1}{4} (by A) + \frac{5}{b} (by B) + \frac{1}{5} (by A) = 1

Hence, \frac{1}{2} + \frac{1}{4} + \frac{5}{b} + \frac{1}{5} = 1

\therefore \frac{10+5+4}{20}+\frac{5}{b}=1

\therefore \frac{19}{20}+\frac{5}{b}=\frac{20}{20}

\therefore \frac{5}{b}=\frac{1}{20}

\therefore b=100days

(Ans: 4)

Estimated Time to arrive at the answer = 75 seconds.

Using Technique

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Presently A works for a total of 10 + 5 + 4 days, i.e 19 days. A alone can finish the work in 20 days. This means that contribution of B is equivalent to saving 1 days work of A or \frac{1}{20} of the total work. B contributes this \frac{1}{20} of the work by working for 5 days, so in 1 day, B will do \frac{1}{100} of the work. Thus, B will take 100 days to finish the work alone.

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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